Preheat the oven to 375°F (190°C).
Slice the zucchinis lengthwise into roughly 1/4-inch thick planks using a mandolin or a sharp knife.
Arrange the zucchini slices on a baking sheet, drizzle both sides with the olive oil, and season with 2 teaspoons salt, 1/2 teaspoon black pepper, and 1 teaspoon dried oregano.
Roast the zucchini in the preheated oven for 20–25 minutes, until slightly softened and lightly browned; remove and set aside.
In a mixing bowl, combine the cottage cheese, grated Parmesan, shredded mozzarella, and the egg until evenly mixed.
Spread about 1 cup of marinara sauce in the bottom of a casserole pan. Layer half of the roasted zucchini slices over the sauce, then spread half of the cheese mixture over the zucchini.
Repeat the layers: spread another cup of marinara (or as needed), arrange the remaining zucchini, and top with the remaining cheese mixture; reserve any extra marinara for another use.
Cover the pan with foil and bake for 30 minutes, until heated through and the filling is set.
Remove the foil and bake an additional 3–5 minutes to lightly brown the top, then let the lasagna rest for 5–10 minutes before slicing and serving.